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Tagged with discrete-morse-theory morse-theory
5
questions
3
votes
1
answer
229
views
Handle attachment information from Morse function and triangulation
First, allow me to setup the relevant information. It is well known that a Morse function $f:M\to\mathbb{R}$ induces a handle decomposition of $M$.
For simplicity, let's restrict for now to the ...
8
votes
1
answer
173
views
Analog of Cerf theory in PL
Is there an analog of Cerf theory in PL?
More specifically, given two handle decompositions of a PL (relative) cobordism $W$, is it always possible to go from one handle decomposition to the other via ...
9
votes
1
answer
263
views
Smooth Morse function from Forman's discrete Morse function
Let $M$ be a smooth manifold and $K$ a triangulation of $M$, so $K$ is a regular CW-complex and in particular a simplicial complex. Assume that $M$ is compact so $K$ is finite. Let $f\colon K \to \...
6
votes
0
answers
261
views
Existence of a perfect discrete Morse function
Let $X$ denote a regular cell structure on a closed (orientable) $n$-manifold (If it helps, the cells are polytopal and the attaching maps are affine).
Recall that a discrete Morse function on this ...
6
votes
2
answers
507
views
Using Discrete Morse Theory to represent hom classes
In "vanilla" Morse theory, you can construct cycles representing integral homology classes of a smooth manifold from a Morse function on the manifold (by looking at the flow into/out of the critical ...